Minority Report

This is a quick update on the school. I’ve been trying to give the students some of the core concepts they need to help them understand what string theory is, how it works, and what you can do with it. Here’s the really odd thing about all this (and an explanation of the post title): While this is a school on Quantum Gravity, after talking with the students for a while one learns that in most cases the little they’ve heard about string theory is often essentially over 20 years out of date and almost always totally skewed to the negative, to the extent that many of them are under the impression that string theory has nothing to do with quantum gravity at all! It is totally bizarre, and I suspect it is largely a result of things that are said and passed around within their research community.. So there are a few students here and there who have some familiarity with strings, huddling together at times for warmth in a sea of miscommunication, misinformation, and strange preconceptions. Let me be the first to point out that the string community also tends to pass on its prejudices about other Quantum Gravity approaches to its students. But my goodness it does seems extreme to me that an approach that has so many clear benchmarks of success (at achieving goals that at least used to be key objectives) in quantum gravity is treated as an irrelevant backwater by the community that thinks of itself as the main practitioners of quantum gravity. Odd. Anyway, my main message is to try to clearly show that the basics are quite easy to grasp if a student has a decent education in Quantum Field Theory, so they can keep an open mind and my lectures will help them navigate the literature (and the other courses coming up) and then make up their own minds about research paths to follow.

It has to be said that the organizers have made a good effort to have a fair amount of string or string related material on the schedule. My only concern is that with so little time given to basic introduction of the ideas (my three lectures), and with so many preconceptions to surmount, only a limited number of non-string students will be paying attention by time the later material from other lecturers gets into full swing…

There is hope though. A good number of students who have never seen string theory before are telling me (with no prompting) that they are beginning to see how it works, and are asking questions about things they’ve been told elsewhere, allowing me to explain the actual facts, give examples, clarifications, and point to lots of juicy results in the literature. They’re also talking to each other, including some of the students who work on strings, informing each other of their respective approaches… and so maybe they are forming a community of a new generation of scholars that will be less embattled than the current generation seems to be…

I think it is so embarrassing how physicists who study quantum gravities behave, on the whole. Too often it reveals an inability to behave in a genuinely scientific manner: curious while skeptical, honest while imaginative. This is paired with an inability to admit the human component of the scientific enterprise: our reasons for choosing a particular avenue for research are rarely entirely logical. Sometimes we are seduced by an idea we like. The problem isn’t the seduction, which I think is an important part of the imagination aspect. The problem is when people get seduced by different things and then become dogmatic about wanting everyone to feel the same.

When no one has data to really genuinely side with them, from the point of view of actually being scientific, I think they look like fools to walk around claiming that they know anything. Why not just glory in the fact that they are privileged enough to get paid to imagine wondrous things and that we live in an era where some of those ideas will face the scrutiny of actual experimental data?

There’s been a lot of complaining from one side about this kind of behavior and a lot of dismissing the other side for whining. Both sides look terrible and like their egos are more important than discovering the right description of our physical world.

On the plus side, it’s a big deal by itself that you are teaching strings to students who wouldn’t otherwise be exposed to it. I don’t think that would have happened when I was starting grad school.

Not too surprising. If I’m not mistaken, their approach to quantum gravity traces its ancestry to DeWitt’s 1966-7 trilogy. So I would expect that they will readily devour talks by the likes of Ashtekar and Rovelli, while remaining circumspect about a “foreign” approach like strings.

You simply cannot work on quantum gravity today without taking into account or knowing something about string theory, directly or indirectly. If you don’t, it would be a physicist in 1920 trying to discover quantum theory without knowing about Bohr’s theory of stationary states and spectra.
goa

> If I’m not mistaken, their approach to quantum gravity traces
> its ancestry to DeWitt’s 1966-7 trilogy.

I think this is historically accurate – but Bryce himself was more sympathetic towards string theory than loop quantum gravity. While he was not sold on either camp entirely, he did recommend strings over loops to me, when I told him my interests where in quantum gravity and was planning to do my doctoral work.

“Here’s the really odd thing about all this … : While this is a school on Quantum Gravity, after talking with the students for a while one learns that in most cases the little they’ve heard about string theory is often essentially over 20 years out of date and almost always totally skewed to the negative, to the extent that many of them are under the impression that string theory has nothing to do with quantum gravity at all!”

I find it extremely hard to believe that the students at this school are ignorant of claims that string theory is a unified theory including quantum gravity, more likely they’re just unconvinced and more interested in other approaches.

I also find it worrying that AdS/CFT, the most prominent success of string theory in terms of making contact with experiments, only yields approximate results. My impression is that AdS/CFT applied to heavy ion physics was very impressive when the entropy/viscosity ratio was first calculated, but now it’s stagnant and not making more precise predictions to keep heavy ion physicists excited about the subject.

Your comment #1:
This is not about unified theories. Not everyone working in string theory has interest in unified theories. That’s simply irrelevant.

Your comment #2:
I’m afraid you’ll be disappointed if you’re looking for one of those tedious back and forth shouting matches about one approach’s achievements vs another. You will find that elsewhere and it was certainly not the issue I am discussing. Nor will you get me to start making overblown claims about what we can do. I don’t and never have done that. These are all research works in progress, and nobody knows the right answers, so how about we all behave like grown-ups? Please have a look at the special issue of the May Physics today for my very carefully expressed thoughts on the quark-gluon issue. You can find a post on that and several other discussions of work in string theory by looking under the category “string theory” or “research” here in the sidebar.

“I find it extremely hard to believe that the students at this school are ignorant of claims that string theory is a unified theory including quantum gravity, more likely they’re just unconvinced and more interested in other approaches.”

has been plagarized in its entirity from Dr Woit’s blog post. […snip…-cvj]

Unless of course Chris and Dr Woit just happen to compose long sentences precisely the same…

All right, please allow me to rephrase my first question. Can you tell me what (if anything) is standing in the way of string theory describing the kinds of black holes we can observe in our universe? I mean, string theory is a quantum theory of gravity, and gravity is a necessary part of string theory, etc., so surely it must allow us to compute the entropy of such black holes.

Hope I wasn’t shouting in this comment and that I was behaving like a grown up.

Clifford doesn’t have to personally answer all questions about string theory. What I don’t understand is why the entropy of black holes is an interesting subject for quantum gravity? Berkenstein about 40 years ago showed that, to avoid violating the 2nd law of thermodynamics (which states that entropy can’t decrease), black holes must gain entropy when something with entropy like hot gas falls into them. If you want to know the entropy of a black hole, calculate the entropy of the disordered random gas molecules falling into it.

Why use string theory? The only link between black holes and quantum gravity is that black holes have entropy and thus disordered energy (with a temperature), thus they radiate energy (Hawking radiation) until they evaporate down to a very small size. Consequently, after sufficient time, the black hole will radiate away all its energy/mass until it’s down to the Planck scale in size, where conventional wisdom claims that you need quantum gravity to understand the physics. What happens at the Planck scale? Do black holes disappear completely, or do they stop radiating at the Planck scale and leave a fundamental particle behind?

But I can’t understand why anyone is interested in this kind of abject pie-in-the-sky speculation, when there are so many parameters like fundamental particle masses and mixing angles that urgently need explanation. The AdS/CFT correspondence seemed promising for QCD because AdS has a negative cosmological constant (unlike the positive one for dark energy implied from cosmology), implying an attractive force which increases with increasing distance like the gluon antiscreening effect of the strong force between quarks. Nobody has yet used it to solve all the QCD problems (avoiding the divergencies in QCD path integral methods), presumably because it’s hard to specify the CFT in a practical way. In string theory, this is complicated with extra spatial dimensions.

“Has string theory calculated the values of the parameters of the standard model and the cosmological constant? If so, what values do it get?” – Chris

This is a rhetorical question because you must know the answer. String theory is a supersymmetric unification project which even in minimal form has 125 parameters (not just the 19 of the standard model), none of which at present seems predictable by string theory due to the landscape problem. The small positive value of the cosmological constant is similarly unpredicted by string theory. Dr Witten said it was a surprise when it was discovered over a decade ago. The hope of Dr Susskind and others is that string theory has so many parameters or moduli for the compactified extra dimensions, that it comes in a large landscape of roughly 10^500 different states, some of which – by sheer force of the huge numbers of different states – are statistically likely to have small positive cosmological constants. Thus, if you can pick out a string theory with a small positive cosmological constant, it will predict stuff.

In addition, Dr Susskind points out in his book that there is another benefit from this landscape of parallel universes: out of 10^500 parallel universes (miltiverse), ours with all of its fine-tuning of parameters required for the evolution of life (coupling parameters, etc.) is likely to have arisen randomly by sheer chance, just as 10^500 monkeys hammering at typewriters are likely to eventually produce the works of shakespeare without any intelligence. So a string theory multiverse removes the need for a God to fine-tune parameters of particle physics for one universe.

Well, when I, as a (L)QG guy talk to my friends in Strings we find a lot of agreement usually. Mostly on the fact that both approaches are dissapointingly flawed.

That said, QG often came about in an atmosphere where senior people from “the other camp” wrote or said in private that it was nonsense and not worth studying. That’s not the kind of behaviour that fosters an open exchange and interest.

As to the 20 years out of date issue, well I remember that in Loops 05 in Berlin for example the community invited Dijkgraaf to talk about spacetime in Strings, and it was a huge dissapointment, precisely because it just rehashed some old cliches that we all had heard about Strings before.

So not everybody has been as forthcoming and willing to come over and explain (and listen to potentially critical questions) as you! I think it’s great, thanks a lot!

If string theory has something to do with quantum gravity, can you please post the scientific paper that demonstrates the relation? If all those physicists are so ignorant, then I suggest that you inform them on your blog. Just post the link.

I think that you misunderstood me. I did not say that you were not behaving like a grownup. Not for asking a question or any other reason. That would be silly, and I don’t think I’ve given you any reason to assume that was my intent. I an sorry if you took it that way – perhaps I wrote too hastily between sessions here at the school… I was, as in my main post, talking about the tone of the discussion in the larger communities, and the kinds of silly arguments and so forth that you often find online.

I hope this doesn’t become a shouting match but I would like to respond to Chris’s questions.

The most relevant work on astrophysical black holes is Strominger et al on the “hidden conformal symmetry” in the Kerr/CFT duality, which maps a rotating nonextremal black hole to a (1+1)-dimensional conformal field theory associated with the axis of rotation. It’s very much work in progress but it looks very exciting.

The quark-gluon plasma I will leave to Clifford.

Finally, “Has string theory calculated the values of the parameters of the standard model and the cosmological constant? If so, what values do it get?” In one of Heckman and Vafa’s papers they say (and I assume this is an authoritative assertion, given the eminent authors) that there are no existing realizations of the standard model in string theory with *stabilized moduli*. The moduli are the parameters of the compactification. So the situation is that there are several known ways in which one might qualitatively realize the standard model in string theory (qualitative = same gauge group and representations, etc), and any specific choice of geometry, fluxes, branes will determine observed properties like mass, *but* these realizations all exist only at a certain level of approximation, and it is an open question as to whether these vacua are stable when all effects are taken into account. At Strings 2010, for example, moduli stabilization was an item in the list of things to do in the F-theory GUT research program. I would like to think that by the end of the year we will have an F-GUT model which matches all known particle-physics and cosmological data (including dark energy), but I can’t guarantee that.

The predictive capabilities of string theory are often called in question. I would say, first, it is of some significance if string theory can just match all available data. Certainly, people once hoped that string theory would have a unique ground state and everything would follow from that, but now we have the notion of an inflating universe with different physics realized in different domains. It is possible that this is just how reality is. The answer is not to accept or reject this picture according to personal taste; the task first of all is to confirm that this is indeed what string cosmology implies. The next task is to truly understand the dynamics of such a situation, and which vacua are preferred. Finally, one wants to know whether the vacua that look like what we see are common, uncommon, or not present at all. That is what it will take to get a prediction out of a chaotic-inflationary string cosmology. Meanwhile, one can still investigate those backgrounds which appear to be stable, and look for something resembling local reality, and this process itself is predictive, in the sense that there are constraints on what is possible. A lot is possible, but it’s not “anything goes”.

String theory is a multi-decade research program and its secrets will not be uncovered all at once. It’s very likely, but not fully confirmed, that it can at least *match* reality, in a quantum framework that includes gravity, and that alone makes it incredibly important. The larger questions require long-term progress and I won’t guess how long that will take.

Hi, Clifford, I think you has missed that, if those belonging to the small Mexican string community agree with you in the assessment of the work of those doing “quantum gravity” in Mexico, they (the Mexican stringy people, MSP) will not care to attend that Morelia school or sending there their students, having the opportunity, for instance, of sending them to Sao Paulo to the Latin American String School 2010.

MSP:- You seem to be concluding that I missed that simple fact based on an odd reading of what I wrote. Where did I say that there should simply be more string theorists at the school? Having knowledge of what is going on in another field that is trying to do exactly what you are trying to do is not equivalent to having to work on it. It would be nice to have more mixing between students following different approaches (I’ve given up on this generation of senior people – and in any case when senior it is harder to find time and motivation to reach far across the borders even if well intentioned) at such schools (and as the days have progressed here in Mexico I’ve seen a lot of such mixing), but that won’t come entirely on its own. There’s a culture of dismissal and suspicion (on both sides, as I said) that is rather odd and unfortunate – that is my central point. The fact that you are talking about the choice of Mexican string theorists to go to one school or another shows part of what I am talking about.

Also, concerning missed points, I remind you that this is an international school held in Mexico (deliberately located in spacetime to match the international gravity meeting following immediately after in nearby Mexico City), not a school for Mexicans. With respect, MSP, I can’t even figure out how you read my post as being about Mexico or Mexican science at all. I don’t even think the words Mexico or Mexican are written anywhere in the post!! Please enlighten me.

Dear Clifford, I appologize for having run into conclusions. As you emphasized, this international school is held in Mexico, not in the moon, and in Mexico “an approach that has so many clear benchmarks of success (at achieving goals that at least used to be key objectives) in quantum gravity is treated as an irrelevant backwater by the community that thinks of itself as the main practitioners of quantum gravity”.
It was easy to get confused and think that you were talking about the situation of Mexicans students. And indeed, that is typically the situation for those students working under the direction of Mexican members of that and related communities of high energy physics. But in other places and circunstances, like the Latin American School, one will easily find Mexican students well aware of what is being doing in string theory or eager to learn about it.

Moving beyond Mexico, I can’t agree more in the benefits of regular meetings between communities working in common topics from different perspectives. But for these meetings to be productive, there should exist a good will of discussing scientifically the scientific results of both sides. This, when talking about ST and LQG, is unfortunately very uncommon, and it typically ends in wasting of time. I can’t be sure, of course, but I think that many members of each commnunity feel threatened by the perspective of the “rivals” obtaining a fundamental result in quantum gravity. It leads to the situation you mentioned (and I cited) above which, of course, can be used to describe, exactly, what the other community also does.

So, “The fact” of “the choice of Mexican string theorists to go to one school or another”, thought indeed odd and unfortunate, maybe just shows that Mexican string theorists do not wish to waste their time. May be…

(1) You say, and I quote, “It was easy to get confused and think that you were talking about the situation of Mexicans students.”

I say… Really?!. In other words, I disagree. Let me point out again the lack of any reference to Mexico or Mexican physicists in the entire post. But perhaps I am wrong and, bizarrely, everyone reading the post took me to be simply trashing Mexican physics instead of making the larger point I’ve been making (on this blog and elsewhere) publicly for many years now. Just in case, I will simply say that I am sad you took it that way and I apologize for giving you the slightest reason for thinking I was talking about “Mexican physics” (and while at the same time being their guests, to boot…).

(2) As to whether it is a waste of time for Mexican string theorists to have gone…. how about you have a chat with the Mexican string theory students who are at the school when they come back later in the week. Presumably as an MSP you will be at the GR meeting they are all going to after the school? Maybe also talk to the students from Brazil, Colombia, the USA, Switzerland, Italy, and several other places that I met there who seemed to be having a great time talking with me and with others about strings and LQG and many other things, as far as I could see. Perhaps it was all entertainment? A novel type of company for watching World Cup games with? Or perhaps more?

First be clear that I’m not an active researcher. I’m still learning string theory… That said, F-GUTs are based initially on an approximation in which gravity is neglected. You postulate certain arrangements of branes in the compact dimensions, and the spectrum of particles arises from excitations on the branes and at their intersections. This appears to provide a framework in which the standard model can be realized, by specifying angles between branes, various fluxes, and so on. You can also get the dark matter this way. That just leaves the cosmological constant; but it also remains to be shown that when you reintroduce gravity (closed strings) to the picture, these approximations are still valid. It’s always possible that the neglected effects will upset the constructions.

But those effects are also relevant for moduli stabilization and for setting the cosmological constant. Part of the research is heading in this direction, and it’s quite a vigorous sub-sub-field, which is why “I would like to think that by the end of the year” we will have examples of F-GUT models which are phenomenologically complete and nonperturbatively stable.

“what’s the difference between this and what you said above? I thought you thought there’s a chance we can match observed data by the end of the year.”

The contrast is between just matching data and *predicting* all the standard model parameters. The models may make a few qualitative new predictions (e.g. that the GUT coupling constant is 1/n for some integer n), and a fully specified brane geometry (etc) will indeed explain where the numbers all come from; but the geometry itself will not be unique. It will still be a matter of building a model to match experiment, rather than deducing *everything* from the one primordial equation or principle. To do the latter, we may have to master those bigger issues to do with inflation, the landscape, and dynamical and/or anthropic selection of vacua.

As a QG guy, I say I must side with fh. Quantum gravity will require far more novel ideas than fairly conservative approaches such as LQG and string theory are willing to offer. It has even pushed a genius like Chris Isham (and he knows virtually all approaches to quantum gravity inside out) to reconsider the question ”what is a thing?”, another example is ‘t hooft who dares to rethink quantum mechanics (and there are plenty of other examples). My best guess is that a new mathematical revolution will offer new perspectives, but it may take a while. The same thing happened for Einstein and Heisenberg when developping GR and QM, they all used brand new mathematics.

You may be right. However, picking a promising approach according to taste can lead you to unexpected places. Sometimes even the right answer. It is the way things always proceed. You start with what you know and work out. Isham should do what Isham does, and others should do what suits them.

Well, I agree and disagree at the same time, every new revolution took a genuinely new physical idea, but it is true that working in the same old approaches ultimately led to the general feeling that a new idea was needed. It is usually only after the invention that the arguments come why the idea was necessary. For example in Einstein’s time, nobody dreamt of a generally covariant field theory; support for the neccesity of general covariance came from a more modest point of view only later one when people realized that a Lorentz invariant quantum field theory for the graviton required something like a metric field which transforms under (infinitesimal) coordiate transformations.

Now as a general relativist, I do not understand the wish for something like (quantum) Lorentz transformations (unitary operators on Hilbert space ) since it doesn’t mean anything physically (it is not connected to a Noether charge expressed in terms of the dynamical fields). Nevertheless particle physicists take these operators for granted and define particles according to their eigenstates. As a relativist, such strategy is unacceptable, and one would expect say string theory to do better and come up with novel ideas about what a particle is (bob wald for example thinks it is a deep question, and consistently stresses the field viewpoint). Like Isham puts it, we have to reconsider what a thing is. Such issues are very physical because they reflect the symmetries of the theory and therefore predictions of it.

My suspicion is that quantum theory will have to be reformulated so that it does not depend anymore on a classical background spacetime (If you do not believe it does, I can immediately propose an elementary exercise which will convince you otherwise). There are plenty of other worries I have but it appears to me that answers to such questions will genuinely require novel ideas. Mostly, if you say something like this to string theorists, you get very hostile attitudes and I regret this.

Yes, but those genuinely new physical ideas did not come out of the blue. They did not come from sitting on a mountain thinking “deep thoughts” in isolation. They came from examining what was currently known and using known tools and ideas to lead to new ones. Different people will find their way using the tools that seem right to them.

Finally, you seem to be someone who understands subtlety and nuance, so do not fall into the usual business of assuming all string theorists are the same. Treat them as individuals.

Hi, that’s true, for example in the case of general relativity, the idea that a ‘local’ theory with no action at a distance should replace Newtonian gravity was 300 years old. But nobody knew how to do it. In retrospect, the first cornerstones came from the theory of special relativity which was first thought to be a mere artifact of Maxwell’s equations. Einstein saw that differently, but what really made the difference was the brand new development of differential geometry by Eli Cartan who realized that the trajectories of free physical objects did not have to satisfy Euclid’s axioms. I am sure that Einstein would have never thought about this himself, actually from his correspondence with Cartan it becomes clear that the latter had to explain him several issues several times Without the personal assistance of Cartan, Hilbert would have been one of the greatest physicists of all times. In that respect, it is of no surprise to me that the grandmaster of string theory is in fact a mathematician.

You seem to be a fair guy, so let me ask a question about something which I consider to be a counterintuitive statement in string theory. It concerns quantized string theory on a curved background, now as far as I know, you perform a weak field approximation in which you perturb around a flat background and the result is that ‘consistency’ in first order requires your background to be Ricci flat. Now, there appear to be several possiblities here : (a) either this demand is an artifact from the perturbative approach (you are simply calculating the wrong stuff), this resembles the argument some people still uphold towards the non-perturbative renormalizability of gravity (b) it is a genuine physical effect and consistency would require to extend the string action by introducing non – trivial couplings to higher derivatives in the geometry (just as this happens in perturbative quantum gravity where you have to take into account higher curvature terms in the action, step by step) (c) the latter option is not a possibility.

Now apart from that, I have no idea what it has to do with einsteins theory, it is just a consistency requirement on the background (which makes one wonder if string theory is really background independent). That something like the Einstein tensor emerges is almost inevitable. I am just a simpe guy, so this remembers me about something I know, which is the Klein Gordon equation. There exists an infinite number of possibilities to write a free Klein Gordon equation on a curved spacetime (where mass terms are introduced by curvature invariants). The model circulating the most is of the type where there is only a coupling to the Ricci scalar (and I presume there was a deeper reason for this, but I somehow forgot). Now, without a coupling to the Ricci scalar, you might say that locally, a solution to the KG equation is arbitrary well approximated by a solution on flat spacetime. But with the Ricci (mass) term this is not the case anymore! So very different physics locally … I wonder whether such ambiguities might also exist in string theory done properly.

A really naughty suggestion (for example) would be to couple the Ricci tensor to the string kinetic term and ‘screw’ causality (causality might not be really screwed, the causal tensor is then just different from the metric tensor) – which is possible by symmetry by the way, general covariance doesn’t forbid you to do this -. That makes me wonder, if we would to the same in general relativity coupled to matter, one could get classically ”euclidean phases” for matter for ‘big’ ricci tensors while we would say that the geometry is Lorentzian. Isn’t that a daring suggestion (it might even make inflation unneccary)? I guess you would need a new constant of nature to do this.

To answer your first question, you must think in terms of the Hamiltonian formalism. Take for example Klein Gordon field theory in a curved (or flat if that makes it easier for you) spacetime. Usually, you pick out a foliation of spacetime where the hypersurfaces of constant ‘t’ are spacelike. Now, one first instance where the background comes into play is that the foliation must be spacelike *everywhere* otherwise (if it would become null somewhere) the Legendre transform would become singular (but that is not really the point). Now, in the Hamiltonian formalism fields with equal time coordinates, but with different space coordinates have trivial Poisson Brackets amongst them. Classically, this means zip, nada, nothing, it is just a way to facilitate the writing down of the field equations. However, quantum mechanically, it becomes a physical statement : two operators at spacelike distances do commute, so measurements at those two locations do not influence each other. Given all what I said until now, it is easy to prove that the background structure, taken together with coordinate independence of the field equations suffices to prove that field operators commute at spacelike separated events. You do not need Lorentz invariance or so for that (so forget the textbook derivations). But now, you might do something silly (but entirely legitimate) : suppose the background structure does not matter and choices of hypersurfaces are free to be made, then just foliate spacetime by hypersurfaces which have mixed signature (say) – ++ (in four dimensions), so your ‘t’ becomes space. From the Hamiltonian point of view, there is nothing wrong with that and the Legendre transform is completely well defined (becomes nowhere singular). Quantum mechanically, what you get is (a) a theory which does not satisfy causality (on flat spacetime it is not even Lorentz invariant) (b) the notion of particle becomes ill defined (even on Minkowski) (you have imaginary modes as wel as operators which have no particle interpretation). So, the commutation relations are thightened to the spacetime geometry. But in general relativity, the spacetime geometry is dynamical so there is no apriori way to impose the commutation relations. There is a small loophole in this argument and CDT is one example of that, but (in that approach and more in general) it seems to me that this induces a preffered folation of space time (a preferred time) which is unphysical from the relativistic point of view and certainly brakes diffeomorphism covariance. Moreover, in a quantum geometry – if I can speculate for a moment – one would expect the notion of spacelike and timelike to fade, more likely one would speak of vectors which can once be measured as being timelike and another time as being spacelike. So, (I am not the only one who thinks this), it appears to me that generalizing quantum mechanics will involve getting a better insight into the commutation relations.

To answer your second question : no I have no idea, if I would, I would be an absolute genius (which I am not). There is one approach I know of which tries to come to such thing, and that involves the work of Rafael Sorkin on quantum measure theory and dynamical (anhomomorphic) logic. I have the greatest respect for that, but they still have a long way to go.

In answer to your questions: What you stated is simply (and well known to be) the low energy approximation to perturbative string theory. There’s an infinite set of higher curvature corrections that you don’t put in by hand… they are there at higher energy (shorted distance) and higher loops.

I am not string theorist (I simply once – long ago – read a chunk of the first volume of Green, Schwarz and witten), so bear with me for a moment. So, if I understand you correctly, you have a perturbative version of quantized string theory which works on ANY background (right?) – then, these corrections are in no sense small and probably your perturbation series doesn’t converge. If so, then comments regarding Einsteins equations being satisfied (and yes they are made) become completely obscure to me. A question would be then if ALL corrections allowed by general covariance are allowed since then – non perturbatively – and in regimes of strong curvature, you would get transitions to ”non – Lorentzian phases” in the matter sector as I described to you earlier. I doubt wheter you would understand that from the viewpoint of perturbation theory.

Actually, did you not end up then in a similar situation as perturbative quantum gravity 30 years ago, a theory with an infinite number of free coupling constants? I thought we kind of dismissed that one for such reasons … Or, is there just a finite number of independent free coupling constants ? Also, I think all terms allowed by symmetry SHOULD be incorporated, otherwise your theory seems to be rather arbitrary. That’s one lesson I could accept from the perturbative game.

These corrections are in no sense small? Where did that come from? There are two well defined length scales – the one set by the tension of the string and the one set by the scale you’re working at (distance, energy) Tune the dimensionless ratio to be small to get low energy or long distance. That’s the regime in which the field equations pop out (also, you’re at tree level in quantum loops).

When not in that regime, this is where we’d go over to what would be considered to be a breakdown of smooth spacetime geometry and so forth. And no, you’re of course not doing perturnation theory any more… This is why we’ve been all excited about the non-perturbative string physics we’ve been doing for over 20 years…. it is opening up windows into this exciting stuff.

I don’t know where you got your infinite coupling constants from. All of the first part of what I said about perturbation theory is very standard and was covered in that text you read. Have another look, and I think it’ll be very clear. No need to make stuff up about the formalism… it’s all there.

So I guess you did not really anwser my question, my question was wheter the Ricci flatness was an artifact of the perturbative calculation (expansion around minkowski), could be undone somehow by adding higher curvature corrections to the action, or is something genuine for all actions of string theory one can write down in curved spacetime (even nonpertubatively). I thought you meant the second option, but you clearly didn’t. Second, you said that at higher loops, higher curvature corrections (to the action) arise (I guess these are curvature corrections in terms of the Riemann tensor then, since the Ricci tensor must be vanishing), which makes it hard to understand what you mean with the breakdown of smooth spacetime geometry (in some other nonperturbative approaches to quantum gravity I know precisely what it is) – since you still work with a fixed background – and even less with the nonperturbative physics you claim to be doing – since your action contains an infinite number of terms with coupling constants depending on the string constant and energy scale.

Ok. Well, I think I explained it as best I could, given available time. I’m sorry if it was not clear. What I described is intrinsically a perturbative setup, which I urged you to look up, but told you how it was organised. The rest is words, and I’m not interested in arguing over words. In my view, when it stops being practical to refer to a background geometry since there’s a huge family of corrections to it at smaller and smaller scales, corrections that cannot be ignored, I simply call that a breakdown of spacetime geometry, and shift to a non-geometric description. You can call it something else. It does not actually matter what we call it. Perturbation theory -the standard string as a bunch of oscillators regime- is when the quantum gravity aspect can be described as gravitons (closed strings) moving on some background (perhaps with corrections up to some order). (And no, not just perturbing around Minkowski as you say.) But we’ve been able to do much more than that for decades now.

There are several non-perturbative approaches (that I “claim” we are doing – why is it necessary to be so rude?) that have a very different starting point. I’ve talked about some of those in earlier comments too (perhaps in a related thread). The most famous of these is probably AdS/CFT, or gauge/gravity duals more generally, but I also refer you to 8 or 9 years earlier than its appearance with the formulation of what we now call minimal strings. From one point of view, you might say the underlying theme in all these examples is holographic: You formulate a string theory in a large family of dynamical backgrounds (i.e., not a fixed background) without reference to them at all, using the equivalence to a field theory in a non-gravitational background.

To clarify more my question : you can write down an infinite number of generalizations of the Polyakov action to curved spacetime (with an infinite number of independent coupling constants), they are all nonlinear theories of course (this in contrast to the infinite number of generalizations of the free KG theory, but that’s because string theory is not a field theory). ONE of my questions is, would they also lead to constraints on the background perturbatively ?
Do you have a physical reason why you would only consider the action obtained by minimal substitution of the flat space Minkowski action?

I think there was still a misunderstanding, but I guess you wanted to say that the Einstein equation gets higher curvature corrections coupled to the string constant.

As for your second: One way of seeing it is that the generalisation used follows nicely from the form of the vertex operator for emission and absorption of gravitons, suitably exponentiated to create a coherent state type background representing some non-trivial curved background. Nothing stopping you or others from trying other things. Nobody said this was the only thing to try… just that it is one way that seems well motivated and which gives remarkable results. Please try other things if they seem good to you.

You still managed not to answer my question (and the perturbation around minkowski is the one described in Green Schwartz and Witten, I said I was not a string theorist). Their computation tells me one should add the Ricci term into the action from the beginning, then you will get in first order perturbation theory a conformally invariant theory, no (no Ricci constraint)? Am I missing here something?

And I am not rude, I am just astonished by the claims given that we cannot even treat the most simple interacting quantum field theories non perturbatively.

I don’t understand. You asked me two questions and I gave you the answer to the one I could answer and specifically stated that I had no answer to the first. I do not know what other question to answer. I’m trying hard here to be helpful.

Once more, to answer your most recent (and I have answered it already): Start with a string in some arbitrary metric… require that it be quantum mechanically consistent theory preserving the important classical symmetries it had (a standard procedure you do in field theory too)… at lowest energy and tree level you get that you must the metric is not arbitrary, but must satisfy Einstein’s equations. There is a well-ordered infinite family of curvature corrections to this result organized in perturbation theory in powers of the inverse string tension and in the string coupling strength. I have no other answer to this issue but that, since that is the result.
I don’t know anything about any adding of Ricci to the action to begin with…. this is not the case. There is no action in spacetime, for a start (this is string pertubation theory and so you are working with a worldsheet action), and secondly this is a result you get out, not one that you put in.

I suspect that we are talking at cross purposes because (in part) of language. Furthermore, this is a blog, not a textbook. To get more, and for things to be more precise, it makes sense to read some other sources. A quick intro can be found in the early sections of my “D-brane primer” to be found on the arxiv.

I don’t understand what is astonishing about non-perturbative results in field theory or string theory…. The last two decades have seen several advances in extracting useful non-perturbative information about both. Huge amounts in field theory, for example. Again, I recommend the literature. A great deal has happened.

Thanks for your reply. The reason why I am so picky about this is because I find the ‘claim’ amazing. Admittedly, we do not even know how to do interacting quantum field theory on a curved spacetime properly (progress is made however), but certainly nobody would expect such theory to constrain the background! That the ”naive” Polyakov action does constrain the background is simply amazing, and there are three possible conclusions : (a) either our method of computation is wrong (b) we consider the wrong classical action (c) it is so and it is telling something deep. I am not sure which one it is. But anyway, perhaps it is not a complete idiocy to couple the Ricci tensor to the matter kinetic term in classical general relativity.

Well, this is again a case of me posting twice before you reply to the first one. The action I am talking about is the ricci tensor coupled to the string kinetic term (the anomalous conformal term you get out in first order, see GSW p. 171 formula 3.4.25 without the phi), it is of course a wordsheet action (and not the Einstein action as you may think), conformally invariant and locally coordinate invariant with respect to world sheet as well as space time coordinates. So, what I am asking is the following, if I would start from a classical theory containing the Polyakov action with the string coupling constant on one side and the ‘Ricci’ action with another coupling constant on the other, let me quantize this one perturbatively around minkowski background, then would I get a conformal anomaly in first order ? It is really the conformal anomaly, which is expressed in terms of the Ricci tensor on the world sheet, for the polyakov action which forces you to set the ricci tensor to zero. Now, I repeat my question, for this modified action, is there a conformal anomaly in first order?

Well, I kind of did something like that 12 years ago when I was still a PhD student. As I tried to tell you on several occasions, one single calculation is telling different people many different things. You start from Polyakov, do your perturbative business around Minkowski, and arrive at an anomaly in first order (with the ricci action as effective action). To me, this says, you are starting with the wrong action since I have this ”intuition” or ”principle” if you would like to, that I should be able to work around ANY background. Nature allows us to do this, it is the very procedure by which we learn new physics, that we neglect some part and focus on quantizing a subsystem. Only string theory – in your interpretation – would tell us that this procedure is untenable ; and no, these constraints on the background have nothing to do with Einsteins theory of gravitation. So what this calculation told me was that we are in the same situation as perturbative quantum gravity, there diffeomorphism invariance forces you to include all possible action terms (with an infinite number of coupling constants) at least if you trust you perturbative calculations. There, this happens at second order, here it already happens at first order. I have no proof of this but it appeared to me that string theory ‘done properly’ (in my view) would lead us to the same situation. Quantum mechanics, conformal invariance and coordinate invariance would force us to. What I find a real shame is that most string theorists have not even contemplated this possibility and regard this constraining business as a virtue (that really boggles my mind)!! I still uphold the possibility that I am wrong, but someone should explain me then.

So, here you have now a personal motivation of a ”could be” morelia student why (amongst other reasons) I am not really knowing more of string theory beyond that.

To Kim, my education was in mathematical physics and relativity. If you want to know more about Isham’s view on this question I refer you to his articles on topos theory.

Concerning your previous comment about ‘nonperturbative’ effects in quantum field theory, I guess you are talking about instanton *approximations* and so on. In a very precise sense, that strategy is still perturbative For example, CDT is genuinely non-perturbative, but there you are forced to make computer approximations at some cutoff scale.

I am always amused by this path of reasoning in comment threads like this. The key part of the game is to lay bets on how many steps a commenter will take to go from “I’ve no knowledge of your field”, to “what you’re all doing is wrong”, usually with little or no time spent looking at the literature.

Well, I gave you PHYSICAL arguments why I believe certain results to point in the wrong direction and you chose not to respond to it, actually you admitted not even to have thought about it. So, at least the little bit I know of string theory, it appears I have looked at it from many more sides than you did. And that is what counts !! Indeed physicsts rock, I remember very well how ‘t hooft could shoot virtually all appoaches to the cosmological constant problem in just 5 minutes without even doing a calculation haha